I usually pronounce the h
Same, though almost never in wh unless I'm trying to give a particular impression. And always pronounce it in herb and hotel unless speaking in my local dialect which doesn't use h at all.
Would you pronounce 'gentleman' and 'gentlemen'
Not really. The distinction is almost inaudible.
but the backwards a makes no sense...
It's a tricky one. There's that, there's the one that looks like the letter æ and a few others. The sound differs. I've found that some Poles (especially ones who did English courses at Warsaw university in the 80s/early 90s - I met their "famous" and genuinely excellent teacher and he spoke like Dame Celia Volestrangler [worth looking out on YouTube] so they probably got it from him) pronounce it in a ridiculously exaggerated way, cet rather than cat. It sounds almost South African or like someone from the Channel Islands. There's also a snobbishness inherent in Polish language and society which leads to a distorted idea of what's "correct" or not when speaking. I've seen people correct each other while speaking which would just lead to a headbutting where I'm from.
phonetics
phonemics
There are a few sounds that are awkward enough to give linguists nice doctorates to frame on their wall.